How is this CPT code in functions.php adding a hidden "products" category?

Question

Here is the code that I modified from https://www.wpbeginner.com/wp-tutorials/how-to-create-custom-post-types-in-wordpress/

/*
* Creating a function to create our CPT
* just drop this in functions.php inside your theme file basically...
* You replaced all 'twentytwenty' with 'twentyseventeen'
*/

function custom_post_type() {

// Set UI labels for Custom Post Type
    $labels = array(
        'name'                => _x( 'Products', 'Post Type General Name', 'twentyseventeen' ),
        'singular_name'       => _x( 'Product', 'Post Type Singular Name', 'twentyseventeen' ),
        'menu_name'           => __( 'Products', 'twentyseventeen' ),
        'parent_item_colon'   => __( 'Parent Product', 'twentyseventeen' ),
        'all_items'           => __( 'All Products', 'twentyseventeen' ),
        'view_item'           => __( 'View Product', 'twentyseventeen' ),
        'add_new_item'        => __( 'Add New Product', 'twentyseventeen' ),
        'add_new'             => __( 'Add New', 'twentyseventeen' ),
        'edit_item'           => __( 'Edit Product', 'twentyseventeen' ),
        'update_item'         => __( 'Update Product', 'twentyseventeen' ),
        'search_items'        => __( 'Search Product', 'twentyseventeen' ),
        'not_found'           => __( 'Not Found', 'twentyseventeen' ),
        'not_found_in_trash'  => __( 'Not found in Trash', 'twentyseventeen' ),
    );

// Set other options for Custom Post Type

    $args = array(
        //'label'               => __( 'products', 'twentyseventeen' ),
        'description'         => __( 'Products and reviews', 'twentyseventeen' ),
        'labels'              => $labels,
        // Features this CPT supports in Post Editor
        'supports'            => array( 'title', 'editor', 'excerpt', 'author', 'thumbnail', 'comments', 'revisions', 'custom-fields', ),
        // You can associate this CPT with a taxonomy or custom taxonomy. 
        'taxonomies'          => array( 'category', 'tag' ),
        /* A hierarchical CPT is like Pages and can have
        * Parent and child items. A non-hierarchical CPT
        * is like Posts.
        */  
        'hierarchical'        => false,
        'public'              => true,
        'show_ui'             => true,
        'show_in_menu'        => true,
        'show_in_nav_menus'   => true,
        'show_in_admin_bar'   => true,
        'menu_position'       => 5,
        'can_export'          => true,
        'has_archive'         => true,
        'exclude_from_search' => false,
        'publicly_queryable'  => true,
        'capability_type'     => 'post',
        'show_in_rest' => true,

    );

    // Registering your Custom Post Type
    register_post_type( 'products', $args );

}

/* Hook into the 'init' action so that the function
* Containing our post type registration is not 
* unnecessarily executed. 
*/

add_action( 'init', 'custom_post_type', 0 );

I created a category called "shop" and I want these CPT "products" to display in my "shop" category so that when you visit domain.com/shop you see a list of them.

I have added "category" capability to taxonomies, and I can select the shop category when creating a new product, but the permalink is always only ever domain.com/products/product-name

Whenever I create a new product custom post, I fill out the description, add the custom fields, title, select the shop category... and everything seems fine until I press publish... then a "permalink" dropdown section appears within the editor, and I am told that I can see the product at domain.com/products/product-name ... when I never selected a products category... and a products category doesn't even exist/never existed!!!

What gives?

If i visit domain.com/shop there is nothing to be seen.

And if I visit domain.com/shop/product-name I am redirected to domain.com/products/product-name (which displays fine by the way).

Any idea where this ghost category called "products" is originating from?

Why is the editor not respecting my desire to place a product in the "shop" category? And instead placing it in it's own "products" category (that doesn't even exist/was never created inside the wordpress admin dashboard).

The only edit I have made to any php code is adding the single function inside my theme's functions.php file.

I even updated/flushed the permalinks settings by re-saving on the custom permalinks section of the dashboard.

Thank you.

EDIT: I believe I may be missing the "rewrite" arg? As explained here: https://developer.wordpress.org/reference/functions/register_post_type/

'rewrite'
(bool|array) Triggers the handling of rewrites for this post type. To prevent rewrite, set to false. Defaults to true, using $post_type as slug. To specify rewrite rules, an array can be passed with any of these keys:

Answer 1

This is the normal behaviour of a custom post type. Any post type other than pages and posts has the post type name in the URL. So for this URL:

https://example.com/products/product-name/

"products" is the post type. Not the category. Similarly, when registering a post type, if has_archive is set to true, then all Products will be automatically viewable at:

https://example.com/products/

The rewrite and has_archive properties can be used to change which slug is used for each for these. For example, if you set:

'has_archive' => 'shop',
'rewrite'.    => [
    'slug'       => 'product',
    'with_front' => false,
],

Then the products archive URL will be:

https://example.com/shop/

And the individual products' URL will be:

https://example.com/product/product-name/

In neither of these cases do you need a "product" or "shop" category.